Without being too direct and asking your age, I'd love to know when you were at school, because what you have written about tables sums up how rubbish teaching (at least in maths) has been for far too long. I would guess after the end of the 1980s? Simple motto for teaching anything, don't make things more complex than they need to be. Special 'methods' for this, that and the other invariably seem to introduce as many problems as they solve.
There's a reason why for hundreds of years times tables were learned by rote. Because it works. Rote learning has its limited place and this is, very much, it. What the hell is the finger method? I learned my tables 40+ years ago in a night (the bribe was a prize for the first to be able do 1 - 12 x 1 - 12 - I got a creme egg - yay!). Can still recite them today (and can rapidly fill in memory gaps through mental arithmetic) and use that ability on a very regular basis.
And the idea that you are either good at English or at maths, but not both is a terrible concept to promulgate. It is simply encouraging that idea that if you are good at English, it's ok to be bad at maths. If you genuinely struggle, fair enough, it is what it is, but never, ever pass on the idea that being bad at maths is normal, even kind of 'cool'. Being able to do the basics (arithmetic, percentages, even trig) easily is normal - as normal as being able to construct a coherent sentence. Just tonight I used some trig to work out how to shape a piece of wood to make a modification to my greenhouse - when you know how it's amazing how often these kind of things come in useful.
I'm a scientist and mathematician at heart, but hopefully you can tell from my writing, that my English ain't that piss poor either. Same goes for every research scientist I ever worked with. All had great skills with language, and some weren't bad with the old figures neither (yes, I'm aware...).